Let \(\text{g}(S) \in \mathbb {N}\cup \lbrace \infty \rbrace \)  equal the genus of \(S\) . The classification states that the triple \((\text{g}(S),E(S), E^g(S))\)  uniquely determines \(S\)  up to homeomorphism. For more details on the classification and on the definition of the spaces of ends, see [1]}.
